Concept explainers
Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
15. Is Echinacea Effective for Colds? Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections.” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). We want to use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, does echinacea appear to have any effect on the infection rate?
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Chapter 9 Solutions
Elementary Statistics (13th Edition)
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- Cigarette Smoking A researcher found that a cigarette smoker smokes on average 29 cigarettes a day. She feels that this average is too low. She selected a random sample of 8 smokers and found that the mean number of cigarettes they smoked per day was 30. The sample standard deviation was 2.3. At a 0.10, is there enough evidence to support her claim? Assume that the population is approximately normally distributed. Use the critical value method and tables. Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho: |(Choose one) Oarrow_forwardst 3 4 25 26 27 28 on 29 K Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. a. Identify the null and alternative hypotheses for this test. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate. O A. Ho: P₁ = P2 H₁: P₁ P2 OB. Ho: P₁ P2 H₁: P₁ P2 OC.…arrow_forwardtest the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Cardiac Arrest at Day and Night A study investigated survival rates for in-hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and were discharged (based on data from “Survival from In-Hospital Cardiac Arrest During Nights and Weekends,” by Peberdy et al., Journal of the American Medical Association, Vol. 299, No. 7). We want to use a 0.01 significance level to test the claim that the survival rates are the same for day and night. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, does it appear that for in-hospital patients…arrow_forwardQuestion content area top Part 1 For the α and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. α=0.01, p-value=0.10 Question content area bottom Part 1 Choose the correct conclusion below. A. Do not reject the null hypothesis since the p-value is not less than the value of α. B. Reject the null hypothesis since the p-value is less than the value of α. C. Reject the null hypothesis since the p-value is not less than the value of α. D. Do not reject the null hypothesis since the p-value is less than the value ofarrow_forwardWhat are the hypotheses for the test? A. H0: β1≠0 and Ha: β1=0 B. H0: β1=0 and Ha: β1<0 C. H0: β1=0 and Ha: β1>0 Your answer is not correct. D. H0: β1=0 and Ha: β1≠0 This is the correct answer. What is the test statistic? t= (Round to two decimal places as needed.) Find the P-value. P-value= (Round to three decimal places as needed.) Part 4 Which of the following is the correct conclusion for the hypothesis test? A. Do not reject H0; the data provide sufficient evidence to conclude that x is useful for predicting y. B. Reject H0; the data do not provide sufficient evidence to conclude that x is useful for predicting y. C. Do not reject H0; the data do not provide sufficient evidence to conclude that x is useful for predicting y. Your answer is correct. D. Reject H0; the data provide sufficient evidence to conclude that x is useful for predicting y. Part 5 b. Find a 95%…arrow_forward19% of deaths among male adults can be attributed to heart diseases. Is this percentage different among residents in Sonoma County? State the Null and Alternative hypothses. H0:H0: ? μ p Select an answer > = ≠ < Ha:Ha: ? μ p Select an answer < = > ≠arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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